IEEE 802.11p has been chosen as the standard for vehicular communications, which is identical to the widely used 802.11a. In 802.11p a default channel spacing of 10 MHz is proposed as opposed to the commonly used 20 MHz spacing in 802.11a to provide better protection against longer delay spreads. It has been shown in “C. Mecklenbräuker, A. Molisch, J. Karedal, F. Tufvesson, A. Paier, L. Bernadó, T. Zemen, O. Klemp, and N. Czink, “Vehicular channel characterization and its implications for wireless system design and performance,” Proceedings of the IEEE, vol. 99, no. 7, pp. 1189-1212, 2011.” and “T. Zemen, L. Bernadó, N. Czink, and A. Molisch, “Iterative time-variant channel estimation for 802.11p using generalized discrete prolate spheroidal sequences,” IEEE Transactions on Vehicular Technology, vol. 61, no. 3, pp. 1222-1233, 2012.”, that the length of the cyclic prefix (CP) and sub-carrier spacing satisfy the design guidelines of an OFDM system for the measured vehicular channels (values of delay, Doppler spreads). However, the training data in 802.11p originally designed for 802.11a is designed for relatively static devices and indoor use. In vehicular communications large vehicular velocities, dynamic environment, and long packet sizes of around 400 bytes mean that the channel impulse response can change significantly within one OFDM frame, see e.g. “L. Bernadó, T. Zemen, F. Tufvesson, A. Molisch, and C. Mecklenbräuker, “Delay and doppler spreads of non-stationary vehicular channels for safety relevant scenarios,” IEEE Transactions on Vehicular Technology, no. 99, 2013.”. Robust channel estimates for the whole frame are required for ensuring desired low Frame Error Rates (FER) for traffic safety application.
To address the high frame error rate due to non-robust channel estimation, solutions using iterative methods and post-ambles have been proposed by “T. Zemen, L. Bernadó, N. Czink, and A. Molisch, “Iterative time-variant channel estimation for 802.11p using generalized discrete prolate spheroidal sequences,” IEEE Transactions on Vehicular Technology, vol. 61, no. 3, pp. 1222-1233, 2012.”
To the best of authors' knowledge the MAC and PHY layer functionalities of an 802.11p transceiver are implemented in the chip and the layers above them are software defined which can be modified with a software update. Also, since 802.11p uses outside the context of a basic service set communication, encryption and authentication are not performed by the MAC layer. As a consequence the data from the layer above the MAC layer enters the PHY layers unchanged with the addition of headers and CRC-32 checksum of fixed lengths.
System Model and 802.11p Frame Structure
The physical layer of 802.11p uses orthogonal frequency-division multiplexing (OFDM) with N=64 subcarriers and a CP of length NCP=16. Among the 64 subcarriers, 48 are allocated for data, 4 are allocated for pilots and 12 are null subcarriers. A channel spacing of 10 MHz results in OFDM symbol duration of TSYM=8 μs which includes a cyclic prefix of 1.6 μs. 802.11p standard supports eight different modulation and coding schemes, see e.g. ““IEEE standard for information technology—telecommunications and information exchange between systems local and metropolitan area networks—specific requirements part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications,” IEEE Std 802.11-2012, pp. 1-2793, 2012, Table 18.4”; the scheme with QPSK mapping and code rate 1/2 is adapted for the safety applications and is important to take into consideration.
The known encoding process of an 802.11 OFDM symbol is illustrated in FIG. 1, which illustrates a block diagram of an 802.11p transmitter. Data bits are scrambled and encoded using a rate 1/2, (1718, 1338) convolutional code. Higher coding rates are achieved using puncturing. The encoded bits are divided into groups of NCBPS bits, where NCBPS is the number of coded bits per OFDM symbol. Bits in each group are interleaved using a two stage interleaver. The interleaved bits are mapped to the constellation  resulting in complex valued symbols. The complex valued symbols and the pilots are mapped to the data subcarriers and the pilot subcarriers of an OFDM symbol, respectively. Following which, an N-point inverse Discrete Fourier Transform (DFT) is performed to obtain time-domain signal and a cyclic prefix of NCP samples is added to form an OFDM symbol. For specific details of the various blocks in the transmitter the readers are referred to ““IEEE standard for information technology—telecommunications and information exchange between systems local and metropolitan area networks—specific requirements part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications,” IEEE Std 802.11-2012, pp. 1-2793, 2012.”, Ch. 18”.
Assigning the data symbol positions to the set  and the pilot positions to the set , the frequency-domain symbol mapped to the kth subcarrier in the mth OFDM symbol is given byS[m,k]=D[m,k]+P[m,k]
where D[m, k] and P[m, k] are the data and the pilot symbols respectively at the kth subcarrier in the mth OFDM symbol, such that P[m,k]=0, ∀[m,k]ε and D[m,k]=0, ∀[m,k]ε. The time-domain samples obtained after the N-point inverse DFT is given bys[m,n]=IDFTN(S[m,k])
Consider the wireless channel with a discrete-time impulse response given byh[n]=Σl=0L-1αlδ[n−τl],
where αl is the complex path gain of the lth tap, l is the delay of the lth tap and L is the total number of taps. Assuming that the maximum excess delay of the wireless channel is shorter than the length of the cyclic prefix and the channel impulse response does not change during transit time of one OFDM symbol, the received samples of the mth OFDM symbol after discarding the CP can be expressed asr[m,n]=s[m,n]Nh[n]+w[m,n], 
Where  is the N-point circular convolution, w[n] are independent and identically distributed (iid) time-domain complex AWGN samples with zero mean and variance σwt2. The frequency-domain symbols carried by the sub-carriers after the N-point DFT operation at the receiver are given byR[m,k]=DFTN(r[m,n])R[m,k]=H[m,k]S[m,k]+W[m,k]
where, H[m, k] is the channel frequency response at the kth sub-carrier of mth OFDM symbol and W[m, k] are the frequency domain complex AWGN samples with mean zero and variance σwt2. The IDFT and DFT operations are suitably scaled to preserve the energy of the signal.
Since the vehicular channels are time varying, the channel impulse response varies within one OFDM symbol resulting in inter carrier interference (ICI) which is not included in the above described model. However, the effect of ICI introduced due to channel variations within one OFDM symbol on the performance of the system is small and is neglected.
A. 802.11p Frame
FIG. 2 shows a standard 802.11p frame in subcarrier-time grid showing the position of the pilots and the data symbols. A frame begins with two identical OFDM symbols referred to as long training (LT) symbols. SIGNAL symbol carries the information regarding the length of the packet and the modulation and coding scheme used. SIGNAL is always encoded using the rate 1/2, (1718, 1338) convolutional code without puncturing and uses BPSK signaling. SIGNAL field is followed by the OFDM symbols corresponding to the data. A sequence of 10 identical short symbols spanning over duration of 2TSYM is prefixed to the frame (not shown in the figure), this sequence is used at the receiver for signal detection and synchronization. The number of OFDM symbols in the standard frame beginning with the two LT symbols is denoted as M.
A generic non-iterative receiver for decoding the 802.11p frames is shown in FIG. 3. Perfect frequency and sampling synchronization is assumed. The CP of the OFDM symbol is discarded and an N-point DFT is performed to obtain the frequency domain symbols. The frequency domain symbols are input to the channel estimation block. The channel estimation block uses the received symbols and the inserted pilot symbols to obtain the channel estimates Ĥ[m,k] for the whole frame. Channel equalization is performed using a Minimum Mean-Square Error (MMSE) equalizer; the output of the equalizer is given by
            S      ^        ⁡          [              m        ,        k            ]        =                              R          ⁡                      [                          m              ,              k                        ]                          ⁢                  H          ^                *                  [                      m            ,            k                    ]                                      σ          wf          2                +                                                                        H                ^                            ⁡                              [                                  m                  ,                  k                                ]                                                          2                      .  
The equalized symbols Ŝ[m, k] are then input to the chain of demodulator, deinterleaver, decoder, and descrambler.